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Full text of "Analytical Mechanics"

EQUILIBRIUM OF RIGID BODIES
37
corresponding product for the other couple. In order, for instance, that the rigid body A, Fig, 28, be in equilibrium, we must have
FD = F'D'.
Therefore the product FD is the measure of the torque of the couple formed by the forces F and  F, the lines of action of which are separated by the distance D. Thus denoting the torque of a couple by G, we have                                               FlG- 2S-
G~FD.                                    (I)
The distance D is called the arm of the couple and the plane of the forces the plane of the couple.
44.   Unit Torque.  The torque of a couple whose forces are one pound each and whose arm is one foot is the unit of torque.    The symbol for the unit torque is the Ib. ft.
45.   Vector Representation of Torque.  Torque is a vector magnitude and is represented by a vector which is perpen-
FIG. 29.
dicular to the plane of the couple. The vector points away from the observer when the couple tends to rotate -the body in the clockwise direction and points towards the observer when it tends to rotate the body in the counterclockwise direction, Fig. 29. In the first case the torque is considered to be negative and in the second case positive.